Probabilistic forecasting using stochastic diffusion models, with applications to cohort processes of marriage and fertility
Demography, 50:1, 237-260 (2013)
We study prediction and error propagation in the Hernes, Gompertz, and logistic stochastic diffusion models and use them to forecast demographic cohort processes. We develop a unified framework in which the models are linearized with respect to cohort age and predictions are derived from an underlying linear process. For prediction variance we develop a Monte Carlo estimator which can be used for a wide class of underlying linear processes. For the case of random walk with drift we develop an analytic prediction variance estimator. The variance estimators allow the forecaster to make precise the level of within-model prediction uncertainty. In addition, the analytic variance estimator provides insights into the sources of prediction uncertainty. Applications to marriage and fertility rates illustrate the usefulness of the new methods, and extend them to simultaneous forecasting of multiple cohorts and to processes restricted by factors such as declining fecundity.